The two managers have exchanged barbs over the last fortnight, dating back to Conte describing Mourinho as "a little man" for his past touchline antics following a thinly-veiled swipe from the Portuguese.
Conte went as far as labelling the feud 'personal' earlier this week after a fresh attack from Mourinho, this time bringing up a match-fixing charge from the Chelsea manager's time in Italian football.
Speaking to reporters on Friday evening, however, the ex-Blues boss claimed that it is time to stop the personal attacks.
"I think when a person insults another you can expect a response or you can expect contempt. Silence," he told reporters. "The first time he insulted me I had a response that touched a point where I know he really feels hurt.
"Then he insulted me for a second time but now I change. Now contempt. For me contempt means end of the story."
Mourinho and Conte will come face to face on the Old Trafford touchline next month, as United play host to Chelsea in the Premier League on February 25.